Advanced Search
MyIDEAS: Login to save this paper or follow this series

Testing Linearity in Cointegrating Relations with an Application to Purchasing Power Parity

Contents:

Author Info

Abstract

This paper develops a linearity test that can be applied to cointegrating relations. We consider the widely used RESET specification test and show that when this test is applied to nonstationary time series its asymptotic distribution involves a mixture of noncentral chi^2 distributions, which leads to severe size distortions in conventional testing based on the central chi^2. Nonstationarity is shown to introduce two bias terms in the limit distribution, which are the source of the size distortion in testing. Appropriate corrections for this asymptotic bias leads to a modified version of the RESET test which has a central chi^2 limit distribution under linearity. The modified test has power not only against nonlinear cointegration but also against the absence of cointegration. Simulation results reveal that the modified test has good size infinite samples and reasonable power against many nonlinear models as well as models with no cointegration, confirming the analytic results. In an empirical illustration, the linear purchasing power parity (PPP) specification is tested using US, Japan, and Canada monthly data after Bretton Woods. While commonly used ADF and PP cointegration tests give mixed results on the presence of linear cointegration in the series, the modified test rejects the null of linear PPP cointegration.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1541.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1541.

as in new window
Length: 44 pages
Date of creation: Dec 2005
Date of revision:
Publication status: Published in Journal of Business and Economic Statistics (January 2010), 28(1): 96-114
Handle: RePEc:cwl:cwldpp:1541

Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC

Order Information:
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Nonlinear cointegration; Specification test; RESET test; Noncentral chi^2 distribution;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Peter C.B. Phillips & Joon Y. Park, 1999. "Nonstationary Binary Choice," Cowles Foundation Discussion Papers 1223, Cowles Foundation for Research in Economics, Yale University.
  2. Vitaliano, Donald F., 1987. "On the estimation of hospital cost functions," Journal of Health Economics, Elsevier, vol. 6(4), pages 305-318, December.
  3. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  4. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation for Research in Economics, Yale University.
  5. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  6. Saikkonen, Pentti & Choi, In, 2004. "Cointegrating Smooth Transition Regressions," Econometric Theory, Cambridge University Press, vol. 20(02), pages 301-340, April.
  7. Philip Hans Franses & Dick van Dijk, 2006. "A simple test for PPP among traded goods," Applied Financial Economics, Taylor & Francis Journals, vol. 16(1-2), pages 19-27.
  8. Simon Peters, 2000. "On the use of the RESET test in microeconometric models," Applied Economics Letters, Taylor & Francis Journals, vol. 7(6), pages 361-365.
  9. Porter, Richard D. & Kashyap, Anil K., 1984. "Autocorrelation and the sensitivity of reset," Economics Letters, Elsevier, vol. 14(2-3), pages 229-233.
  10. Ermini, Luigi & Granger, Clive W. J., 1993. "Some generalizations on the algebra of I(1) processes," Journal of Econometrics, Elsevier, vol. 58(3), pages 369-384, August.
  11. Moshiri, Saeed & Cameron, Norman E & Scuse, David, 1999. "Static, Dynamic, and Hybrid Neural Networks in Forecasting Inflation," Computational Economics, Society for Computational Economics, vol. 14(3), pages 219-35, December.
  12. Bowden,Roger J. & Turkington,Darrell A., 1990. "Instrumental Variables," Cambridge Books, Cambridge University Press, number 9780521385824, April.
  13. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
  14. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  15. Lothian, James R & Taylor, Mark P, 1996. "Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 488-509, June.
  16. Siu Fai Leung & Shihti Yu, 2001. "The sensitivity of the RESET tests to disturbance autocorrelation in regression analysis," Empirical Economics, Springer, vol. 26(4), pages 721-726.
  17. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
  18. Breitung, Jörg, 1998. "Rank tests for nonlinear cointegration," SFB 373 Discussion Papers 1998,65, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  19. Lo, Ming Chien & Zivot, Eric, 2001. "Threshold Cointegration And Nonlinear Adjustment To The Law Of One Price," Macroeconomic Dynamics, Cambridge University Press, vol. 5(04), pages 533-576, September.
  20. Peter Pedroni, 2001. "Purchasing Power Parity Tests in Cointegrated Panels," Department of Economics Working Papers 2001-01, Department of Economics, Williams College.
  21. Grilli, Vittorio & Kaminsky, Graciela, 1991. "Nominal exchange rate regimes and the real exchange rate : Evidence from the United States and Great Britain, 1885-1986," Journal of Monetary Economics, Elsevier, vol. 27(2), pages 191-212, April.
  22. Kapetanios George, 2003. "Bootstrap Neural Network Cointegration Tests Against Nonlinear Alternative Hypotheses," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(2), pages 1-16, July.
  23. Peter C.B. Phillips, 1982. "ERA's: A New Approach to Small Sample Theory," Cowles Foundation Discussion Papers 645, Cowles Foundation for Research in Economics, Yale University.
  24. Linda F. DeBenedictis, & David E. A. Giles, 1998. "Robust Specification Testing in Regression: The FRESET Test and Autocorrelated Disturbances," Econometrics Working Papers 9806, Department of Economics, University of Victoria.
  25. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series no6, Institute of Economic Research, Seoul National University.
  26. Alan M. Taylor, 2000. "A Century of Purchasing-Power Parity," NBER Working Papers 8012, National Bureau of Economic Research, Inc.
  27. Rustam Ibragimov & Peter C.B. Phillips, 2004. "Regression Asymptotics Using Martingale Convergence Methods," Cowles Foundation Discussion Papers 1473, Cowles Foundation for Research in Economics, Yale University.
  28. Thursby, Jerry G, 1981. "A Test Strategy for Discriminating between Autocorrelation and Misspecification in Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 63(1), pages 117-23, February.
  29. O'Connell, Paul G. J., 1998. "The overvaluation of purchasing power parity," Journal of International Economics, Elsevier, vol. 44(1), pages 1-19, February.
  30. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-79, March.
  31. Peter C.B. Phillips, 1999. "Descriptive Econometrics for Nonstationary Time Series with Empirical Illustrations," Cowles Foundation Discussion Papers 1219, Cowles Foundation for Research in Economics, Yale University.
  32. repec:nsr:niesrd:153 is not listed on IDEAS
  33. Ken Froot & Kenneth Rogoff, . "Perspectives on PPP and Long-Run Real Exchange Rates," Working Paper 32027, Harvard University OpenScholar.
  34. Rudiger Dornbusch, 1985. "Purchasing Power Parity," NBER Working Papers 1591, National Bureau of Economic Research, Inc.
  35. Zhijie Xiao & Peter C.B. Phillips, 2001. "A CUSUM Test for Cointegration Using Regression Residuals," Cowles Foundation Discussion Papers 1329, Cowles Foundation for Research in Economics, Yale University.
  36. Jeffrey A. Frankel and Andrew K. Rose., 1995. "A Survey of Empirical Research on Nominal Exchange Rates," Center for International and Development Economics Research (CIDER) Working Papers C95-051, University of California at Berkeley.
  37. Serena Ng & Pierre Perron, 2002. "PPP May not Hold Afterall: A Further Investigation," CEMA Working Papers 83, China Economics and Management Academy, Central University of Finance and Economics.
  38. Robert de Jong, 2004. "Nonlinear estimators with integrated regressors but without exogeneity," Econometric Society 2004 North American Winter Meetings 324, Econometric Society.
  39. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-80.
  40. Peter C.B. Phillips, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation for Research in Economics, Yale University.
  41. Baghestani, Hamd, 1991. "Application of the RESET test to the original Andersen-Jordan equation," Journal of Macroeconomics, Elsevier, vol. 13(1), pages 157-169.
  42. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
  43. Mussa, Michael, 1976. " The Exchange Rate, the Balance of Payments and Monetary and Fiscal Policy under a Regime of Controlled Floating," Scandinavian Journal of Economics, Wiley Blackwell, vol. 78(2), pages 229-48.
  44. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
  45. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  46. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
  47. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-79, August.
  48. repec:cup:macdyn:v:5:y:2001:i:4:p:533-76 is not listed on IDEAS
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2006. "Purchasing Power Parity: The Irish Experience Re-visited," Trinity Economics Papers tep200615, Trinity College Dublin, Department of Economics.
  2. Chaohua Dong & Jiti Gao, 2014. "Specification Testing in Structural Nonparametric Cointegration," Monash Econometrics and Business Statistics Working Papers 2/14, Monash University, Department of Econometrics and Business Statistics.
  3. Vadim Marmer, 2005. "Nonlinearity, Nonstationarity and Spurious Forecasts," Econometrics 0503002, EconWPA, revised 15 Dec 2005.
  4. repec:wyi:journl:002195 is not listed on IDEAS
  5. Haiqiang Chen & Ying Fang & Yingxing Li, 2013. "Estimation and Inference for Varying-coefficient Models with Nonstationary Regressors using Penalized Splines," SFB 649 Discussion Papers SFB649DP2013-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. Chaohua Dong & Jiti Gao & Dag Tjostheim & Jiying Yin, 2014. "Specification Testing for Nonlinear Multivariate Cointegrating Regressions," Monash Econometrics and Business Statistics Working Papers 8/14, Monash University, Department of Econometrics and Business Statistics.
  7. Liew, Venus Khim-Sen & Ling, Tai-Hu & Chia, Ricky Chee-Jiun & Yoon, Gawon, 2012. "On the application of the rank tests for nonlinear cointegration to PPP: The case of Papua New Guinea," Economic Modelling, Elsevier, vol. 29(2), pages 326-332.
  8. Qiying Wang & Peter C.B. Phillips, 2006. "Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1594, Cowles Foundation for Research in Economics, Yale University.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1541. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.